Nonoscillation, oscillation and convergence of a class of neutral equations

Delay-dependent criterionfor asymptotic stability of a class of neutral equations

“…Recently, the asymptotic stability of equation (1) has been discussed in [2,3], and the delayindependent sufficient conditions for the stability have been presented. In the work [2], only the case a = ~-is considered.…”

“…In the work [2], only the case a = ~-is considered. In general, abandonment of information on the delay causes conservativeness of the stability criteria especially when delays are small.…”

Global exponential stability for a class of neural networks

“…So far, numerous sufficient conditions ensuring asymptotic stability for Eq. (1) have been established in the literature [6][7][8][9]. However, those results cannot ensure the global exponential stability for Eq.…”

Bifurcation analysis in a neutral differential equation

“…Delay differential equations of various types that contain (E) as a special case have been proposed by many authors for the study of the dynamical characteristics of neural networks of Hopfield type (see [5,8,[21][22][23] and the references cited therein). A majority of results on Eq.…”

“…(E) deal with stability, oscillatory, non-oscillatory as well as asymptotic behaviors of solutions such as global attractability of zero. An earlier result of El-Morshedy and Gopalsamy [5] proved, under the assumption 0 < −pe aτ < 1 and ap + b < 0 that solutions of (E) oscillate about the zero if either one of the following conditions is satisfied:…”